Lower bounds for norms of products of polynomials via Bombieri inequality
- Autores
- Pinasco, Damian
- Año de publicación
- 2012
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper we give a different interpretation of Bombieri´s norm. This new point of view allows us to work on a problem posed by Beauzamy about the behavior of the sequence $S_n(P)=sup_{Q_n}, [PQ_n]_2$, where $P$ is a fixed $m-$homogeneous polynomial and $Q_n$ runs over the unit ball of the Hilbert space of $n-$homogeneous polynomials. We also study the factor problem for homogeneous polynomials defined on $zC^N$ and we obtain sharp inequalities whenever the number of factors is no greater than $N$. In particular, we prove that for the product of homogeneous polynomials on infinite dimensional complex Hilbert spaces our inequality is sharp. Finally, we use these ideas to prove that any set ${z_k}_{k=1}^n$ of unit vectors in a complex Hilbert space for which $sup_{Vert z Vert=1} vert langle z, z_1 angle cdots langle z, z_n angle vert$ is minimum must be an orthonormal system.
Fil: Pinasco, Damian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina - Materia
-
BOMBIERI'S INEQUALITY
BOMBIERI'S NORM
GAUSSIAN MEASURE
PLANK PROBLEM
POLYNOMIAL
PRODUCTS OF LINEAR FUNCTIONALS
UNIFORM NORMS INEQUALITIES - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/196933
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Lower bounds for norms of products of polynomials via Bombieri inequalityPinasco, DamianBOMBIERI'S INEQUALITYBOMBIERI'S NORMGAUSSIAN MEASUREPLANK PROBLEMPOLYNOMIALPRODUCTS OF LINEAR FUNCTIONALSUNIFORM NORMS INEQUALITIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we give a different interpretation of Bombieri´s norm. This new point of view allows us to work on a problem posed by Beauzamy about the behavior of the sequence $S_n(P)=sup_{Q_n}, [PQ_n]_2$, where $P$ is a fixed $m-$homogeneous polynomial and $Q_n$ runs over the unit ball of the Hilbert space of $n-$homogeneous polynomials. We also study the factor problem for homogeneous polynomials defined on $zC^N$ and we obtain sharp inequalities whenever the number of factors is no greater than $N$. In particular, we prove that for the product of homogeneous polynomials on infinite dimensional complex Hilbert spaces our inequality is sharp. Finally, we use these ideas to prove that any set ${z_k}_{k=1}^n$ of unit vectors in a complex Hilbert space for which $sup_{Vert z Vert=1} vert langle z, z_1 angle cdots langle z, z_n angle vert$ is minimum must be an orthonormal system.Fil: Pinasco, Damian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Mathematical Society2012-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/196933Pinasco, Damian; Lower bounds for norms of products of polynomials via Bombieri inequality; American Mathematical Society; Transactions of the American Mathematical Society; 364; 8; 8-2012; 3393-40100002-9947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/tran/2012-364-08/S0002-9947-2012-05403-1/S0002-9947-2012-05403-1.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:51:03Zoai:ri.conicet.gov.ar:11336/196933instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:51:04.212CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Lower bounds for norms of products of polynomials via Bombieri inequality |
title |
Lower bounds for norms of products of polynomials via Bombieri inequality |
spellingShingle |
Lower bounds for norms of products of polynomials via Bombieri inequality Pinasco, Damian BOMBIERI'S INEQUALITY BOMBIERI'S NORM GAUSSIAN MEASURE PLANK PROBLEM POLYNOMIAL PRODUCTS OF LINEAR FUNCTIONALS UNIFORM NORMS INEQUALITIES |
title_short |
Lower bounds for norms of products of polynomials via Bombieri inequality |
title_full |
Lower bounds for norms of products of polynomials via Bombieri inequality |
title_fullStr |
Lower bounds for norms of products of polynomials via Bombieri inequality |
title_full_unstemmed |
Lower bounds for norms of products of polynomials via Bombieri inequality |
title_sort |
Lower bounds for norms of products of polynomials via Bombieri inequality |
dc.creator.none.fl_str_mv |
Pinasco, Damian |
author |
Pinasco, Damian |
author_facet |
Pinasco, Damian |
author_role |
author |
dc.subject.none.fl_str_mv |
BOMBIERI'S INEQUALITY BOMBIERI'S NORM GAUSSIAN MEASURE PLANK PROBLEM POLYNOMIAL PRODUCTS OF LINEAR FUNCTIONALS UNIFORM NORMS INEQUALITIES |
topic |
BOMBIERI'S INEQUALITY BOMBIERI'S NORM GAUSSIAN MEASURE PLANK PROBLEM POLYNOMIAL PRODUCTS OF LINEAR FUNCTIONALS UNIFORM NORMS INEQUALITIES |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
In this paper we give a different interpretation of Bombieri´s norm. This new point of view allows us to work on a problem posed by Beauzamy about the behavior of the sequence $S_n(P)=sup_{Q_n}, [PQ_n]_2$, where $P$ is a fixed $m-$homogeneous polynomial and $Q_n$ runs over the unit ball of the Hilbert space of $n-$homogeneous polynomials. We also study the factor problem for homogeneous polynomials defined on $zC^N$ and we obtain sharp inequalities whenever the number of factors is no greater than $N$. In particular, we prove that for the product of homogeneous polynomials on infinite dimensional complex Hilbert spaces our inequality is sharp. Finally, we use these ideas to prove that any set ${z_k}_{k=1}^n$ of unit vectors in a complex Hilbert space for which $sup_{Vert z Vert=1} vert langle z, z_1 angle cdots langle z, z_n angle vert$ is minimum must be an orthonormal system. Fil: Pinasco, Damian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina |
description |
In this paper we give a different interpretation of Bombieri´s norm. This new point of view allows us to work on a problem posed by Beauzamy about the behavior of the sequence $S_n(P)=sup_{Q_n}, [PQ_n]_2$, where $P$ is a fixed $m-$homogeneous polynomial and $Q_n$ runs over the unit ball of the Hilbert space of $n-$homogeneous polynomials. We also study the factor problem for homogeneous polynomials defined on $zC^N$ and we obtain sharp inequalities whenever the number of factors is no greater than $N$. In particular, we prove that for the product of homogeneous polynomials on infinite dimensional complex Hilbert spaces our inequality is sharp. Finally, we use these ideas to prove that any set ${z_k}_{k=1}^n$ of unit vectors in a complex Hilbert space for which $sup_{Vert z Vert=1} vert langle z, z_1 angle cdots langle z, z_n angle vert$ is minimum must be an orthonormal system. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-08 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/196933 Pinasco, Damian; Lower bounds for norms of products of polynomials via Bombieri inequality; American Mathematical Society; Transactions of the American Mathematical Society; 364; 8; 8-2012; 3393-4010 0002-9947 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/196933 |
identifier_str_mv |
Pinasco, Damian; Lower bounds for norms of products of polynomials via Bombieri inequality; American Mathematical Society; Transactions of the American Mathematical Society; 364; 8; 8-2012; 3393-4010 0002-9947 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/tran/2012-364-08/S0002-9947-2012-05403-1/S0002-9947-2012-05403-1.pdf |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
American Mathematical Society |
publisher.none.fl_str_mv |
American Mathematical Society |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
reponame_str |
CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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13.070432 |